Question

An object, initially at rest, is subject to an acceleration of 34 m/s^2. How long will it take for that object to travel 3400 m?

a) 20 seconds
b) 100 seconds
c) 200 seconds
d) 2,000 seconds

Answer 1

Using the kinematic equation for uniformly accelerated motion, we find that an object starting from rest and accelerating at 34 m/s^2 will take approximately 14.14 seconds to travel 3400 m, not matching any of the provided answer choices.

Step-by-step explanation:

The student is asking how long it will take for an object with an initial velocity of 0 m/s, subject to an acceleration of 34 m/s2, to travel a distance of 3400 m. To solve this, we can use the kinematic equation for uniformly accelerated motion:

s = ut + (1/2)at2

Where s is the distance, u is the initial velocity, a is the acceleration, and t is the time. Since the object starts from rest (u = 0), the equation simplifies to:

s = (1/2)at2

Plugging in the values we get:

3400 m = (1/2) × 34 m/s2 × t2

Solving for t gives us:

t2 = × 6800 / 34

t2 = 200

t = √200

t = 10 √2 ≈ 14.14 s

Therefore, none of the answer choices (a) 20 seconds, (b) 100 seconds, (c) 200 seconds, or (d) 2,000 seconds are correct. The object will take approximately 14.14 seconds to travel 3400 m when accelerating at 34 m/s2.